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Infinitesimals in Modern Mathematics, Jonathan Hoyle, MAA Seaway Section, October 20, 2007 2:30 PM Room B11-107

[Slides (HTML)] [Paper (HTML)] [Paper (PDF)] [Slides (PDF)] [Other MAA Seaway Fall 2007 sessions]



Fall 2007 Joint Conference between the Mathematical Association of America Seaway Section and the New York State Mathematics Association of Two Year Colleges Region I, hosted by the Monroe County Community College Mathematics Department, October 19-20, 2007.



This talk will tour the various modern mathematical models of infinitesimals. After a brief historical overview of their use by mathematicians over the centuries, modern definitions will be introduced. By extending the ordered field of the reals, Non-Archimedean values appear, and depending upon the construction, standard theorems from analysis may produce very unusual results. An introduction of Nonstandard Analysis will be made first, outlining the constriction of Hyperreals and an overview of interesting results pertaining to this structure. This will be followed by a tour of other mathematical systems involving infinitesimals, including Surreal numbers, Superreal numbers, Super-real fields and Smooth Infinitesimal Analysis.


Link to Infinitesimals in Modern Mathematics

Link to online Presentation of paper

Download Infinitesimals in Modern Mathematics [PDF format, 225K]

Download Presentation introduction [PDF format, 4.9MB]


Link to Fall 2011 Seaway page on Forensic Mathematics and the World Trade Center Project

Link to Spring 2009 Seaway page on Introduction to Surreal Numbers

Link to Spring 2008 Seaway page on Counter-Intuitive Results from the Hyper-reals



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